BRUSSELS — The European Union is stepping up pressure on the United States to add more European countries to the list of those whose citizens can travel across the Atlantic without a visa, holding out the threat of requiring Americans to get visas for trips to Europe if Washington does not agree.

The European Commission is expected to consider on Tuesday whether to change the visa requirements for Americans if their government does not agree to include additional European Union member states — Bulgaria, Croatia, Cyprus, Poland and Romania — on the list of those entitled to visa-free travel.

In the case of Canada, the dispute concerns two of those countries, Romania and Bulgaria.

The escalating dispute comes at a time when Washington is especially concerned about security, in the aftermath of terrorist attacks in Europe and the presence of suspected terrorists in the flow of migrants to the Continent out of the Middle East. Should the commission decide to move toward imposing visa requirements, it could be a blow to trans-Atlantic relations just before a visit to Europe by President Obama and could complicate negotiations on other issues, including a proposed trade deal.

Right now, Americans and Canadians generally can travel to Europe for business and vacations without a visa. But the European Union is insisting that the United States abide by a timetable previously agreed upon among European authorities for adding the five European countries that are not already on the list of those allowed visa-free travel to the United States. The deadline for that change is next week, but no agreement had been reached Thursday evening.

It remains unclear whether Brussels will actually start the process of imposing visa requirements next week. If it did, the change would not go into effect immediately, and there would be a period of up to six months when a majority of Europe’s national governments and the European Parliament could block the move.

The European Commission is made up of 28 representatives from each European Union member state, so that gives representatives from the countries seeking to be added to the visa-free list, like the commissioner for industry, Elzbieta Bienkowska of Poland, a say in the matter.

But the negotiation may have been complicated by recent terrorist attacks involving European citizens who have fought in Syria or been radicalized in Europe, and those assaults highlight the bloc’s vulnerability to rising militancy in an age of easy travel.

That may have made Washington even more reluctant to make travel to the United States easier for more Europeans.

“Over the past months, all sides have intensified their efforts in order to reach tangible and concrete progress,” Mina Andreeva, a spokeswoman for the commission, said in a statement on Thursday. “Our goal is full reciprocal visa waiver with our strategic partners,” she said.

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There are currently 38 countries whose citizens have visa waivers, according to the Department of Homeland Security. The program enables eligible citizens or nationals of designated countries to travel to the United States for tourism or business for stays of 90 days or less without first obtaining a visa.

Some of the European Union countries excluded from the program, like Poland and Cyprus, joined the European Union in 2004, more than a decade ago. Romania and Bulgaria joined in 2007. Croatia became a member in 2013.

But citizens of other countries that joined the bloc in 2004, including Estonia, Latvia and Lithuania, the Czech Republic and Hungary, do have visa-free travel to the United States, and that has helped to generated frustration.

In Bulgaria, the economy minister, Bojidar Loukarsky, told local news media in 2014 that his country would support a trade pact with the United States only if Washington waived visa requirements for his country’s citizens. (A spokeswoman for the Bulgarian Permanent Representation to the European Union suggested on Thursday that the official position of the government in Sofia was more nuanced.)

“No matter what happens with visas, this should not impact trade negotiations with the United States as immigration plays no formal part in those talks,” Marietje Schaake, a Dutch member of the European Parliament, who is on the international trade committee, said in an interview on Thursday.

A holdup in the trade talks now could be harmful to the prospects of a deal, which has already become bogged down in highly technical discussions, particularly because Mr. Obama’s successor may not have the same willingness to reach a deal that opens American markets to more foreign competition. The two sides have been in formal negotiations to reach a partnership to increase growth and to further align their economies since 2013.

Even so, there is pressure from the capitals of major European Union members, including Poland, where a succession of governments has pushed for its citizens to be treated like other nationals of other European Union member countries.

“Polish governments have been lobbying for a long time with the U.S. authorities, in Congress and in the administration, to eliminate this obstacle in traveling to the United States,” said Artur Habant, the spokesman for the Permanent Representation of Poland to the European Union in Brussels.

Poland should be considered “another boring European country,” he said.

According to Mr. Habant, American authorities say they have often had to refuse applicants in Poland, making the granting of visa waivers for all Poles difficult. “This has however never been too convincing to the Polish government, as you can imagine, because they need to protect the interests of the Polish people,” said Mr. Habant. He emphasized that there should be reciprocity because “U.S. citizens have had visa-free travel to Poland for years now,” he said.